In this paper, the influence of PM[Formula: see text] on children’s respiratory diseases is taken as the main research focus. Based on the real monitoring data of children’s respiratory diseases in Anhui province, the traditional model is modified substantially, leading to the establishment of two mathematical models. First of all, considering that the PM[Formula: see text] changes over time, a nonautonomous air pollution-related disease model is constructed to study its permanence and extinction. Furthermore, regarding lag days of PM[Formula: see text] exposure, an air pollution-related disease model with the lag effect is installed and its local and global stabilities and Hopf bifurcation are investigated. Meanwhile, the above two models are numerically simulated, respectively. Our study demonstrates that the threshold conditions of permanence and extinction are obtained by the nonautonomous air pollution-related disease model, and the optimal parameters are obtained through the annual revision of the data by integrating the mathematical model, such that the number of children with respiratory diseases in the future can be checked and predicted. Also our study finds that the lag days of PM[Formula: see text] exposure have little effect on children with respiratory diseases in the air pollution-related disease model with a lag effect, but the PM[Formula: see text] has a tremendous influence on the number of patients. Once the lag days are combined with the effect of the PM[Formula: see text], it can have a significant impact on the patients’ number, e.g. an emergence of periodic oscillations, with an approximate period of 11 days in Anhui Province, due to the Hopf bifurcation.

中文翻译：

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建模和预测 PM2.5 对儿童呼吸系统疾病的影响

本文以PM[公式：见正文]对儿童呼吸道疾病的影响为主要研究重点。基于安徽省儿童呼吸系统疾病的真实监测数据，对传统模型进行了大幅度修改，建立了两个数学模型。首先，考虑到PM[公式：见正文]随时间变化，构建了一个非自治的空气污染相关疾病模型来研究其持久性和灭绝性。此外，关于 PM[公式：见文本] 暴露的滞后天数，安装了具有滞后效应的空气污染相关疾病模型，并研究了其局部和全局稳定性以及 Hopf 分岔。同时，分别对上述两种模型进行了数值模拟。我们的研究表明，通过非自主空气污染相关疾病模型获得持久性和灭绝性的阈值条件，并通过整合数学模型，通过数据的年度修正获得最优参数，使得患有呼吸系统疾病的儿童人数可以检查和预测未来的疾病。我们的研究还发现，在具有滞后效应的空气污染相关疾病模型中，PM[公式：见文]暴露的滞后天数对呼吸系统疾病儿童的影响很小，但PM[公式：见文]具有巨大的影响。对患者数量的影响。一旦滞后天数与 PM[公式：见正文] 的影响相结合，它会对患者数量产生重大影响，例如出现周期性波动，